As the electric power steering control apparatus described above, a device, which calculates a basic control variable based on a detection result of a torque sensor for detecting a steering torque and estimates the steering torque with a configuration that does not use the torque sensor when the torque sensor is abnormal (refer to, for example, Patent Literature 1), has been known. In this kind of electric power steering control apparatus, when the torque sensor has malfunctions, the basic control variable is calculated based on the steering torque estimated based on another signal. However, if a detection cycle of the acquirable estimated steering torque is longer than a detection cycle of the torque sensor, a torque oscillation increases due to a decrease in the detection cycle (a longer detection cycle). To cope with such a problem, Patent Literature 1 stabilizes a control system by subtracting a damping torque set based on a steering angle from the basic control variable.